After generating a new intermediary distribution \(P^j\)  we assign weights to each particle according to [1]}:
\(\omega _{i}^{j+1} = \frac{p(\theta _i^{j+1})}{\sum _{i^{\prime }=0}^N \omega _{i^{\prime }}^j K(\theta _{i}^j | \theta _{i^{\prime }}^{j-1})}\) 
